Problem: Solve for $x$ and $y$ using elimination. ${6x-y = 9}$ ${-5x+y = -6}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {6x-y = 9}\thinspace$ to find $y$ ${6}{(3)}{ - y = 9}$ $18-y = 9$ $18{-18} - y = 9{-18}$ $-y = -9$ $\dfrac{-y}{{-1}} = \dfrac{-9}{{-1}}$ ${y = 9}$ You can also plug ${x = 3}$ into $\thinspace {-5x+y = -6}\thinspace$ and get the same answer for $y$ : ${-5}{(3)}{ + y = -6}$ ${y = 9}$